Thursday, May 29, 2014

What follows is an explanation of a phrase that Hirsch uses
in most of his papers, “hole-electron asymmetry of condensed matter”. The explanation was adapted from one of
Hirsch’s papers[1], that can be found on arxiv as well as Phys. Rev . B.

Hirsch frequently refers to the ‘hole-electron asymmetry of
condensed matter’. In the article entitled
“Electron-hole asymmetry and superconductivity”, he provides a nice picture of
exactly what he means by this phrase. I
adapted the explanation for a presentation I’ll give soon on the H-ray
theory. The slides follow. A more complete and texty explanation can be
found at the link above. The text that
follows below is the very rough draft of some of the vernacular for the
presentation. For those who are die-hard
fans of watching people fumble with practice presentations, I've also posted the first run-through of these slides. The
video is more for my reference than anything else. You’ve been warned :)

In Hirsch’s papers, he talks a lot about something he calls
the hole-electron asymmetry of condensed matter and he has one paper where he
actually describes in a pretty nice way what he means by the hole-electron
asymmetry of condensed matter. Normally when
you’re doing condensed matter physics you can talk about electrons, (negatively
charged particles), or holes. Holes are
taken by al lot of people to mean a lack of an electron so it means a positive
charge where an electron would have been and they talk about them fairly symmetrically. So, for example, they’d say that an electron
current moving to the righ in this picture is the same as a hole current moving
to the left. Almost all their equations
work out great because when you change the sign of the charge on the charge
carrier, you also change the sign of the velocity, and so things like the sign
of the current stay the same. This is
what Hirsch describes as symmetry. You
can’t tell l the difference between holes and electrons in a lot of condensed
matter physics.

When you get to superconductors, this is where Hirsch points
out the hole electron asymmetry. In superconductors,
there are experiments that show that the charge carriers have to be electrons
and can’t be holes. One of them is the
London moment. In that experiment, the
physically rotate a superconductor, like our superconducting cylinder here, and
a magnetic field is created that points (actually down) into the superconductor
if it’s rotating in a counter-clockwise direction. That field points down because the charge carriers
that create the field are electrons, negative charge carriers. If the charge carriers were holes, they would
be positive and the magnetic field would point in the opposite direction. So, what Hirsch means when he says the
hole-electron asymmetry in condensed matter physics is that in superconducting materials,
there are experiments where you can tell that the current involved is a current
of electrons and not a current of holes moving in the opposite direction. The reason we believe it’s electrons is that the
electrons are moving along with the superconducting cylinder, (lagging just a
bit), and when the electrons rotate this way they create a magnetic field that
is anti-parallel to the angular velocity vector, which is what we see.